Friday, December 11, 2015

Positive Feedback Loops: The Other Roads to Ruin

Positive feedback like, “Nice post!” is always welcome, but positive feedback that gets stuck in a loop can have catastrophic results.

The most memorable experience of positive feedback is the head-splitting screech that fills an auditorium when the PA system experiences feedback. Someone speaks into the microphone and the sound is amplified. Amplified sound from the speakers is picked up by the microphone and amplified again through the speakers and back to the microphone and . . . well, by about the fifth cycle through the amp everyone in the room is holding their hands over their ears and mouthing silent profanities.

The most common experience of a negative feedback loop is your home thermostat that reduces heat when the temperature gets higher. You’d think that a screeching PA system would be negative and a thermostat controlling your home heating and cooling would be positive, but that isn’t how feedback loops are named.

According to one website, a more formal explanation of the difference is this:
“Positive feedback loops enhance or amplify changes; this tends to move a system away from its equilibrium state and make it more unstable. Negative feedback loops tend to dampen or buffer changes; this tends to hold a system to some equilibrium state, making it more stable."
So, when does a retirement income system “tend to move away from its equilibrium state and become unstable”?

To answer that, I'll tell a story about a retired couple in 2007, because I was raised in the South where every question is answered with a story. My story is not strictly true (a long-standing tradition of Southern stories). I will build a composite retired household from personal observations of multiple actual households from that time, some of whom weren't really even retired but, as my grandfather would’ve said with a grin if he were telling this story, “they might'a been.”

Jim and Linda retired in Omaha in 2005. The family seemed well-to-do, but they lived in a large, heavily mortgaged home. Jim had built a small fortune over his working career investing in rental homes, also heavily mortgaged, and most of their retirement income came from those properties. They both had retirement accounts invested in index funds worth about $200,000 and significant income from several CD’s and a money market fund.

Life went pretty much as planned until late 2007 when the stock market began a 50%, 18-month drop, interest paid on safe investments dropped to zero and, worse for Jim and Linda, the real estate market tanked, all simultaneously. Though most people would eventually recover from these crises, Jim and Linda wouldn't – a financial crisis can be a very personal thing.

Market losses aren't the only road to ruin in retirement.
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With the rental income gone and the CD's and money market funds now paying a pitiful fraction of one percent, Jim could no longer afford the mortgage on his home plus the mortgages on fifty or so rental properties so he let the unprofitable rentals go. There were no buyers, so “letting go” meant skipping mortgage payments until the banks foreclosed.

The family’s rental business had drifted into a positive feedback loop wherein foreclosed properties reduced income, which reduced their ability to pay other mortgages, which resulted in more foreclosures, which resulted in even less income. It didn't stop until all the properties, including their home, were foreclosed. In less than a year, Jim and Linda's once-shiny finances looked like PA system feedback sounds.

The couple’s plan had assumed that their portfolio of rental properties was well diversified. Sure, a few of the fifty properties might fail from time to time, but what were the odds that a catastrophic number of them would fail in short order? Incidentally, this is the same assumption that led to the Wall Street collateralized mortgage obligations crisis on a much grander scale and as Jim, Linda and several Wall Street giants soon learned, the correlations had been much higher than they had believed.

Jim needed to sell their stocks, intended to fund decades of retirement, at lower and lower prices as the stock market continued its collapse. The stock market would recover years later, as stock brokers promise it always will, but Jim and Linda wouldn't participate in that recovery. Their stocks had long been sold. The stock market had also entered a positive feedback loop with selling encouraging more selling for a year and a half.

Their retirement planner had told them that they could safely spend 4% of their portfolio value each year, or about $8,000. There was a small chance, around 5%, that a series of poor returns early in retirement would result in their outliving their savings, but an even smaller chance if they spent less when their portfolio declined in value. Unfortunately, they did realize that unlikely poor performance right after they retired.

Jim, Linda and their planner had assumed that spending might need to be reduced during a bad market spell. (We say “spell” in this context a lot in Southern stories. It’s a very versatile word. We can sit for a spell, Uncle Howard can have one of his spells, or in Louisiana we might even cast one.) What they hadn’t considered is that forces other than market volatility – like expense surprises and lost income, for example – might preclude their ability to make those needed spending cuts.

Each year that Jim and Linda spent more than planned from their portfolio increased their probability of ruin. The continual shrinking of their portfolio value as the market fell increased it even more. Soon that probability of ruin was a lot more than the original 5%. An example is provided in the table below.

Their portfolio spending strategy had drifted into a positive feedback loop (that's three if you're keeping score), wherein every year that they overspent from their savings they increased the risk of portfolio ruin, reduced their capacity to recover when the market did, and decreased the amount of spending that would be considered safe the following year, increasing the probability that they would need to overspend yet again. The way to escape this loop would have been to reduce spending from their portfolio. Without the rental income and fixed income interest, they couldn’t.

The good (and coincidentally true) ending to this story is that today, eight years later, all of the households in this composite have recovered to some degree, though one middle-aged couple divorced under the strain. The investment portfolio is gone, as is the real estate wealth, but they have a "spell" to recover because, as I said, none of them were actually retired. The outcome would have been worse had they been. Younger people have more risk capacity and remaining human capital.

Most people survived and completely recovered from these simultaneous stock, interest rate and real estate crashes, but Jim and Linda did not. Had their investment properties not simultaneously tanked, they would have easily survived the bear market and kept their home.

What types of spending shocks can initiate a positive feedback loop? There are several candidates. A late-life divorce can be financially devastating and, though you may imagine them rare, they are not. I am aware of three among my circle of acquaintances over the past five years. (One gentleman was 80 and he married again within a year.)

Unexpected medical expenses, particularly onerous with dementia (see Costs for Dementia Care Far Exceeding Other Diseases), aren't uncommon. Two families within my circle of acquaintances are retired and financially stressed by the high support costs of their grown children who have medical problems. A combination of small underestimates of spending, expected market returns, and longevity could also do the trick in an otherwise survivable economic downturn. (As I showed in 100% Certain That We're Not Sure, there is no certainty that you picked the correct portfolio spending rate to begin with. You may already be overspending.)

Research shows that well-diversified retirement portfolios are unlikely to completely fail as a result of market volatility. (See, for example, Larry Frank.) The portion of the portfolio that is unlikely to disappear is sometimes referred to as a “soft floor.” Stout and Mitchell (download PDF) showed that retirees who reduce spending when their portfolio is stressed can reduce the risk of ruin by 30% to 40%.

These studies don't address spending volatility, however, so they don't predict what happens if retirees, like Jim and Linda, are unable to make the needed spending reductions. Mean reversion and diversification won't save those who can't due to divorce, dementia, debt or dependents.

The positive feedback loops are present in these studies if you look for them carefully. Observe what happens to a portfolio in a constant-dollar spending model and you will see that when a portfolio declines in value and the retiree keeps spending a constant-dollar amount, she increases the risk of portfolio ruin going forward. When this happens several years in a row, the probability of ruin grows quite quickly. In the following table, a 65-year old couple in 1974 with a 50% equity portfolio wishing to spend $52,000 from a $1M portfolio each year would see their probability of ruin nearly triple in five years. (Probability of ruin calculated using Milevsky formula.)

Year Return on 50% Equity Portfolio Portfolio Balance Withdrawal Rate for $52k
of Ruin
Initial 1,000,000 5.0%
1974 -8% 872,160 6.0% 5.2%
1975 -11% 729,942 7.1% 8.5%
1976 18.5% 803,362 6.5% 14.4%
1977 6.5% 800,200 6.5% 10.6%
1978 -4% 718,272 7.2% 14.4%

The table above demonstrates a positive feedback loop that would have developed had the retiree felt it was safe to continue the same amount of spending yearly as the market declined (it isn't), but it would also have developed if the retiree hadn't been able to reduce spending.

Positive feedback loops disappear in dynamic-updating models that assume that the retiree will be able to cut spending when necessary. Since there are no unmet liabilities (overspending) in these models, there are no positive feedback loops. The difference between probabilities of ruin between the two types of models offers an estimate of the risk of not being able to reduce spending.

Stout and Mitchell found that adjusting spending reduces risk of ruin 30% to 40% compared to constant-dollar spending, so we can infer that not adjusting spending is about 43% to 67% riskier than adjusting it. The risk that we will deplete our portfolio because we can't adjust our spending is that 43% to 67% probability times the probability that we won't be able to reduce spending. The probability that we can't is far more difficult to estimate.

We can, however, ballpark that probability by considering our financial risk capacity. If we have lots of money saved relative to our spending needs, we have lots of risk capacity and the odds are better that we won't find ourselves unable to reduce spending from our portfolio when needed. The less savings we have relative to our spending, the greater the likelihood that we may be unable to reduce spending when necessary and the greater the chances that we will trigger a positive feedback loop that ends in ruin.

(Another way to look at risk capacity is your portfolio spending rate. If you only need to spend 1% to 2% annually, you're far safer from spending crises than if you need to spend 4% or more annually.)

Most Southern stories have a moral and this one is no exception. Market volatility isn't the only road to portfolio depletion. Studies that ignore spending risk understate the probability that a retiree will outlive savings.

Here's my intuition: retirees are more likely to outlive their savings as the result of a spending crisis that triggers a downward, self-feeding spiral than they are to outlive their savings as a result of slowly overspending 4% a year instead of 3.5%, especially if they dynamically update their plans. I readily admit I don't have data to back that up, so take it for what it is. I also suspect that long-term persistent overspending and sequence risk are far more likely to result in a permanent loss of standard of living than outright ruin.

Retirement income systems are vulnerable to positive feedback loops that can preclude the option to reduce spending in times of portfolio stress. Nor is retirement uniquely the domain of positive feedback loops. My personal experience with pre-retirement households that ended in personal bankruptcy displayed evidence of loops. Long bouts of unemployment or disability trigger them; consumer debt, divorce and foreclosure combine to finish them, in good stock markets and bad.

Another impression I have is that most of us have far more confidence in retirement models than our understanding of them merits, and "us" includes financial planners. I appreciate models as research and learning tools and as tools that can support a good retirement plan, but I've been building and studying them for perhaps 20 years and the list of their weaknesses is long. They can't predict an individual household's future and they are not by themselves a retirement plan (see Michael Kitces' recent post.)

Positive feedback loops are a characteristic of chaos theory. Is our retirement income system a chaotic system that is normally in equilibrium but can unpredictably be drawn into the influence of a point attractor like ruin? I'm not certain, but I have been doing some research and having some interesting discussions. Check out Retirement Income and Chaos Theory.


  1. Once again a great post ... and a great story (you are Southern)!

    And the moral of the story seems to be to make your best estimate this year and then redo it each and every year after. I can see plenty of class mates over the years who were only thrown rotten curve balls in life and retirement as they envisioned isn't in the cards. Other classmates are just the opposite having better curve balls thrown to them during their lives. Thus everything in life is stochastic and may you stay in the fortunate group rather than the prior.

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  3. Another good article Dirk. You always make me think. I find myself wondering what to do to help reduce positive feedback loops in retirement. You mention several ways -

    Dynamic updating of withdrawal rates.

    Having the ability to reduce spending when necessary.

    Having a high funded ratio (low withdrawal rate 1-2%) to begin with.

    I wonder if there are others you might offer? Ones I might offer include -

    insurance - disability, health and long term care possibly (or at least a plan for LTC expenses)

    floor and upside approach - annuities or TIPS for your floor

    possibly longevity insurance

    proper asset allocation to begin with

    Thanks for another thought provoking blog. Brad

    1. Yes, all of those things, Brad. As I pointed out in 100% Certain, however, you can never know for sure if you have the right asset allocation.

      The key point is that funding retirement with a stock portfolio is probably a lot riskier than most people think. That doesn't mean we shouldn't do it, because most people can't fund retirement with the measly returns of safer investments alone. It does mean that you need a backup plan to survive should your savings be depleted, whether that is caused by poor returns or a spending crisis.

      Thanks for writing, Brad.

  4. Thanks for response Dirk. Yes, stocks are a mixed blessing which is why I lean toward the floor upside approach (as I believe you do), and the mantra - take no more risk than you have the ability, need or willingness to take (or receive a premium for taking). Thanks again Dirk. Brad

  5. Some people may feel comfortable going into retirement with "heavily mortgaged home and rental homes, also heavily mortgaged. To me this is mostly a story of leverage gone bad. Having the home paid off and some actual equity in the rentals would have probably let them survive though probably bruised still.

    1. I agree, John. But every bankruptcy is a story of something gone bad – the housing market, divorce, death, health, fraud – and that something subsequently causing other things to go bad. And, that's the point. You need to plan for things going bad other than the market. Poor market returns can erode your standard of living, but bankruptcy is catastrophic.

      Thanks for writing!

  6. Good article and excellent blog. I have been reading your blog for a couple of years before we retired in early 2015. Your advice has been helpful. Like your last commenter, going into retirement with significant debt that cannot be carried in a market downturn is generally a bad idea! I still have a small mortgage on my house but no other debt. I also created an income stream using the "floor and upside" model that Wayne Pfau writes about.

    Being a municipal retiree I do have a pension and we are holding off taking Social Security until 70. I am naturally conservative and wanted to enter retirement as flexible as possible.

    Thanks again for your work.


    1. David, sounds like you're in pretty good shape for retirement income. If you've read my posts for a while, you know that no one advocates eliminating debt before retiring more aggressively than I do. I have no credit card debt and payed off my mortgage. Debt can be deadly.

      To be perfectly clear, my concern with the previous comment was the statement, "to me this is mostly a story of leverage gone bad." That seems to imply that you don't need to worry about insolvency if you're smart about leverage. I will add, though, that while one of the families was over-leveraged, something I would never recommend, they still wouldn't have failed were it not for a massive failure of Wall Street dealing with collateralized mortgages. Lots of people lost their homes in that scandal.

      While we might say "this is mostly a story of leverage gone bad" for one of the families, we could also say two of the bankruptcies were "mostly stories of marriages gone bad" and one was "mostly a story of a career choice gone bad."

      Every bankruptcy can be explained as something that went bad and avoiding it is hardly ever as simple as not doing dumb things.

      Your retirement strategy seems solid. Thanks for your comment!